This paper introduces a temporal bivariate area-level linear mixed model with independent time effects for estimating small area socioeconomic indicators. The model is fitted by using the residual maximum likelihood method. Empirical best linear unbiased predictors of these indicators are derived. An approximation to the matrix of mean squared errors (MSE) is given and four MSE estimators are proposed. The first MSE estimator is a plug-in version of the MSE approximation. The remaining MSE estimators rely on parametric bootstrap procedures. Three simulation experiments designed to analyze the behavior of the fitting algorithm, the predictors and the MSE estimators are carried out. An application to real data from the 2005 and 2006 Spanish living conditions survey illustrate the introduced statistical methodology. The target is the estimation of 2006 poverty proportions and gaps by provinces and sex.

本文介绍了具有独立时间效应的时态双变量区域级线性混合模型，用于估计小区域社会经济指标。该模型通过使用残差最大似然法进行拟合。得出这些指标的经验最佳线性无偏预测因子。给出了均方误差（MSE）矩阵的近似值，并提出了四个MSE估计量。第一个MSE估算器是MSE近似的插件版本。其余的MSE估算器依赖于参数引导程序。进行了三个仿真实验，旨在分析拟合算法，预测变量和MSE估计变量的行为。2005年和2006年西班牙生活状况调查对真实数据的应用说明了引入的统计方法。